We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finit...

Deep fundamental factor models are developed to automatically capture nonlinearity and interaction effects in factor modeling. Uncertainty quantification provides interpretability with interval est...

Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the subsequent local volatility surface is never considered. In this article, we develop a deep learning approach for interpolation of European vanilla option prices which jointly yields the full surface of local volatilities. We demonstrate the modification of the loss function or the feed forward network architecture to enforce (hard constraints approach) or favor (soft constraints approach) the no-arbitrage conditions and we specify the experimental design parameters that are needed for adequate performance. A novel component is the use of the Dupire formula to enforce bounds on the local volatility associated with option prices, during the network fitting. Our methodology is benchmarked numerically on real datasets of DAX vanilla options.

The era of modern financial data modeling seeks machine learning techniques which are suitable for noisy and non-stationary big data. We demonstrate how a general class of exponential smoothed recurrent neural networks (α-RNNs) are well suited to modeling dynamical systems arising in big data applications such as high frequency and algorithmic trading. Application of exponentially smoothed RNNs to minute level Bitcoin prices and CME futures tick data, highlight the efficacy of exponential smoothing for multi-step time series forecasting. Our α-RNNs are also compared with more complex, “black-box”, architectures such as GRUs and LSTMs and shown to provide comparable performance, but with far fewer model parameters and network complexity.